Theorems · Theorem · field theory

algebraicClosure.eq_restrictScalars_of_isAlgebraic

∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type u_3)
  [inst_3 : Field K] [inst_4 : Algebra F K] [inst_5 : Algebra E K] [inst_6 : IsScalarTower F E K]
  [Algebra.IsAlgebraic F E], algebraicClosure F K = IntermediateField.restrictScalars F (algebraicClosure E K)

If K / E / F is a field extension tower, such that E / F is algebraic, then algebraicClosure F K is equal to algebraicClosure E K.

Defined in

Mathlib.FieldTheory.AlgebraicClosure

Cited by

0 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTowerAlgebra.IsAlgebraic